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(CNN)President Barack Obama on Friday responded to Donald Trump's convention speech, specifically disputing the Republican presidential nominee's view that the country is being threatened by rising crime rates and illegal immigration.

CNN's Reality Check Team of reporters, researchers and editors listened throughout the speech and selected key statements, rating them true; mostly true; true, but misleading; false; or it's complicated.

"We have put unprecedented resources at our border," he said. "Well, it turns out that the rate of illegal migration into the United States today is lower by two-thirds than it was when Ronald Reagan was president. We have far fewer undocumented workers crossing the border today than we did in the '80s or the '90s or when George Bush was president."

In 1986, the number of apprehensions peaked and US Border Patrol picked up more than 1.6 million undocumented immigrants. In the 1990s, more than 1 million people trying to cross the border illegally were apprehended each year.

During Bush's tenure as president from 2000-2008, on average, 1 million undocumented workers were picked up each year.

The numbers of people apprehended crossing the border illegally has been on the decline since Obama took office, and in 2015, US Border Patrol apprehended 337,117 people, the lowest number since 1971.

It is, of course, very difficult to check the total number of people who have tried to cross the border in any given year. The number of apprehensions gives us a good idea, but it also assumes that border patrol's resources and effectiveness have remained somewhat constant over the years. There is also no way to know how many people crossing the border illegally eluded arrest or how aggressive Border Patrol agents are with apprehensions at any given time.

In the early 1990s, there were more than 4,000 Border Patrol agents and fewer physical barriers on the border. Today, the number of agents staffing the border patrol has risen to more than 20,000. Since the 1990s, border patrol has focused on deterring people from trying to cross the border in the first place. CBP says that their expanded capability has "substantially deterred illegal entries," and they say that "the number of Border Patrol encounters with people trying to enter the country illegally dropped by 78% between fiscal years 2000 and 2012."

The number of people apprehended by Border Patrol has been on a general decline since 2005, though there was a slight increase between 2012 and 2014. Since Obama took office in fiscal year 2009, there has been a 39% decrease in apprehensions of people who tried to cross the border illegally. There have been, however, large fluctuations in the number of children and their families and unaccompanied children apprehended on the US-Mexico border. Between fiscal years 2013-2014, there are there was a huge spike in the number of unaccompanied children and family unit subjects apprehended by Border Patrol. The trend slowed the following year, and apprehensions picked back up in the first half of fiscal year 2016 when there were almost as many unaccompanied children and family units apprehended as there were in all of fiscal year 2015.

The reason that people are crossing the border is shifting, said Donald Kerwin, director of the Center for Migration Studies of New York. Fewer people are coming to seek work and more people are seeking refuge from violence or because they are afraid for their lives, which could explain the increase in families and children being apprehended trying to cross the border illegally.

We rate Obama's claim as true based on the best metric we have to measure how many people may be crossing the border, even though it is far from perfect.

Thursday night, Trump warned that dangerous criminals from Central and South America have entered the United States illegally and are at large. We checked those claims as well.

Trump likely got that number from a congressional hearing last December, when Iowa Republican Sen. Chuck Grassley said there were 179,027 undocumented criminal immigrants awaiting removal and at large. While the statistic is more than six months old, and we can't confirm exactly how many of those criminals have been deported, we rate Trump's claim as true.

Trump then conflated criminals with families apprehended at the border.

"The number of new illegal immigrant families who have crossed the border so far this year already exceeds the entire total from 2015," Trump said. "They are being released by the tens of thousands into our communities with no regard for the impact on public safety or resources."

According to the Department of Homeland Security, the number of apprehensions of families on the southwest border has spiked in 2016 but there is no indication that the families are being released en masse. Therefore, our verdict on this claim is true, but misleading.

Trump added, "One such border crosser was released and made his way to Nebraska. There, he ended the life of an innocent young girl named Sarah Root."

Trump was referring to a man from Honduras, Eswin Mejia, who killed Root last January in a drunk driving accident. The incident was a tragedy -- Root had graduated from college hours before the wreck with a 4.0 grade point average -- but Trump's description of the undocumented immigrant's background had inaccuracies. Mejia did not recently arrive in America, as Trump suggested. He has been here since at least 2013. And Mejia did not have a criminal record in Honduras, according to Immigration and Customs Enforcement. These claims are false.

Reality Check: Obama on violent crime rates

By Sonam Vashi, CNN

The President defended his record on crime after Trump claimed that "decades of progress made in bringing down crime are now being reversed by this administration's rollback of criminal enforcement" in his Thursday night speech.

Obama said, "When it comes to crime, the violent crime rate in America has been lowered during my presidency and any time in the last three, four decades. And although it is true that we've seen an uptick in murders and violent crime in some cities this year, the fact of the matter is that the murder rate today, the violence rate today, is far lower than it was when Ronald Reagan was president, and lower than when I took office."

The FBI measures violent crime, which includes murder, rape, robbery and aggravated assault. The violent crime rate in 2014 was the lowest it's been since the mid-1990s, and it has decreased by 15% between 2009, when Obama took office, and 2014, the latest year for which full data is available.

The homicide rate in 2014 was 4.5 per 100,000 people, which was the lowest rate since 1964.

But let's look at larger trends of U.S. violence. Murders increased in the 1960s and 70s, fell midway during Reagan's presidency, peaked in 1991, and then began a sharp decline until the present, according to data from the Bureau of Justice Statistics. The overall violent crime rate has also been steadily declining since the 1990s, according to FBI data.

So, violent crime and homicide rates were already on a downward trend before Obama took office. It's not fair to credit his presidency for any increases or decreases in those rates without noting that larger trend, but Obama is true in saying that violent crime is lower now than in previous decades.

As for the uptick in violence this year in major cities, Trump stated that "homicides last year increased by 17% in America's 50 largest cities. That's the largest increase in 25 years."

We Reality-Checked Trump's claim on the uptick in violence in America's 50 largest cities on Thursday and found that it was true. The Washington Post's WonkBlog analyzed crime data for major cities and found that 770 more people, or 17% more, were killed in 2015 than the previous year, the biggest increase since 1990. Thirteen of the 50 cities analyzed had fewer homicides in 2015 than 2014, but homicides increased overall.

An important caveat: The Post also says that the data shows "no single explanation for the increases and reveals no clear pattern among those cities that experienced the most horrific violence." Additionally, 2015's increase in homicides doesn't reverse the decades of decline in murder rates nationally.